You just need to go around the world fast enough that it’s always one time.
This is actually correct, but not for the reason you might think. It has nothing to do with time zones.
In physics, time is quite literally defined as “what a clock would read”. As you approach the speed of light, time dilation approaches infinity and therefore your rate of proper time approaches zero.
If you reach the speed of light, your rate of proper time exactly equals zero and thus the clock is correct 100% of the time.
There is one caveat: in order to reach the speed of light, your mass must equal exactly zero. In which case you can only travel at the speed of light since deceleration is not possible.
Bearing that in mind, it would be correct from a physics standpoint to claim that a broken clock accurately measures the proper time of a photon (or other massless particle).
Only if you ignore that minutes and seconds exist.
Linear timezones would be weird
It wouldn’t be that far from how it worked before the invention of the railways, each town had its own local time. https://en.m.wikipedia.org/wiki/Railway_time
I don’t think they would even be called timezone! The whole concept falls apart.
It’d be a… timeline? That would be more confusing. You’d be dealing with spatioemporal coordinates just to get to work in the morning.
Time does not go in lines… it goes in circles! That is why clocks are round!
Timefield?
Time spectrum?
At the equator, Earth is nearly 25k miles around. So you need to travel around 1050 mph. The speed of sound is usually under 800 mph, so you’ll be going a good bit faster than this. That is going to be one impressive fuel tank. Still that is a whole lot less than the 17k mph you need to get to the space station.
So, once a day then?
Only at 6pm, all day